18.3 Electric Field
3 min read•june 25, 2024
Electric fields are the invisible forces surrounding charged particles. They describe how electric charges interact, pushing and pulling each other through space. Understanding electric fields is key to grasping the behavior of charged objects and their effects on one another.
This section covers the strength and direction of electric fields, diagrams, and the principle. We'll explore how to calculate and visualize electric fields, and how multiple charges combine to create complex field patterns.
Electric Field
Strength and direction of electric fields
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- () vector quantity describes force per unit at a point in space
- Measured in units of N/C or V/m
- For a (), electric field at distance given by Coulomb's law:
- :
- pointing from charge to point of interest
- Direction of electric field depends on sign of charge:
- Positive charges create electric fields pointing radially outward (protons)
- Negative charges create electric fields pointing radially inward (electrons)
- Strength of electric field decreases with distance from charge ( relationship)
- Moving twice as far from charge reduces field strength by factor of 4
- Electric field of a acts as if all charge concentrated at center (outside the sphere)
- The between charged particles is directly related to the electric field strength
Electric field line diagrams
- Electric field lines visual representation of electric field in a region
- Field lines originate from positive charges and terminate on negative charges
- Density of field lines indicates relative strength of electric field (more dense = stronger field)
- Field lines never cross, implies multiple field directions at single point
- For single point charge:
- Field lines extend radially outward for positive charge (isolated )
- Field lines extend radially inward for negative charge (isolated )
- For two equal and opposite charges ():
- Field lines extend from positive charge to negative charge
- Field lines more concentrated near charges, indicating stronger field (H2O molecule)
- For two equal charges of same sign:
- Field lines extend radially outward from each charge
- Field lines more separated in region between charges, indicating weaker field (two protons)
- Electric field lines provide qualitative understanding of field direction and relative strength
- Do not show exact magnitude of field at any point
- Useful for visualizing field patterns and understanding charge interactions
- is a measure of the electric field passing through a given surface area
Superposition of multiple charges
- Electric field obeys principle of superposition:
- Net electric field at a point due to multiple charges is of individual electric fields created by each charge
- To find net electric field () at a point:
- Calculate electric field () at point due to each charge individually using Coulomb's law
- Add individual electric field vectors to find net electric field:
- When adding electric field vectors:
- Consider both magnitude and direction of each field
- Use vector addition techniques (components, trigonometry) to find resultant field
- Superposition allows calculation of electric fields in complex charge distributions (multiple point charges, charged lines/planes)
- Break problem into simpler parts by considering each charge separately
- Combine individual fields using vector addition to find net field
- Superposition is a powerful tool for analyzing electric fields and forces in electrostatic systems (capacitors, particle accelerators)
Work and Potential Energy in Electric Fields
- done by electric field on a charged particle relates to change in its
- Electric potential energy is the energy stored in a system of charges due to their positions
- Equipotential surfaces are regions where the electric potential is constant
- Moving charges perpendicular to equipotential surfaces requires work against the electric field
Key Terms to Review (26)
Charge: Charge is a fundamental property of matter that is the source of all electrical phenomena. It is the quantity that determines the strength of the electric and magnetic forces between particles or objects. Charge can be either positive or negative, and it is quantized, meaning it comes in discrete amounts.
Charged Sphere: A charged sphere is a three-dimensional object with a uniform distribution of electric charge throughout its volume. The electric field and potential generated by a charged sphere are important concepts in the study of electrostatics.
Coulomb's Constant: Coulomb's constant, also known as the electrostatic constant, is a fundamental physical constant that describes the strength of the electrostatic force between two stationary, electrically charged particles. It is a crucial parameter in understanding the behavior of electric fields and electric potential.
Dipole: A dipole is a pair of equal and opposite electric charges, typically a positive and a negative charge, separated by a small distance. It is a fundamental concept in the study of electric fields and the behavior of charged particles in electric fields.
E-field: The E-field, or electric field, is a vector field that describes the force exerted on a charged particle by the electromagnetic field. It is a fundamental concept in electromagnetism and is crucial for understanding the behavior of charged particles in various contexts.
Electric Dipole: An electric dipole is a separation of positive and negative electric charges within a system, resulting in a net electric field and a potential difference between the two charges. It is a fundamental concept in electrostatics and is essential for understanding various phenomena in the context of electric fields.
Electric Field: The electric field is a vector field that describes the electric force experienced by a charged particle at any given point in space. It is a fundamental concept in electromagnetism that connects the properties of electric charges to the forces they exert on one another.
Electric Flux: Electric flux is a measure of the total electric field passing through a given surface. It represents the number of electric field lines that intersect a surface, and it is a fundamental concept in the study of electromagnetism and the behavior of electric fields.
Electron: An electron is a subatomic particle that carries a negative electric charge and is found in all atoms. Electrons play a crucial role in the study of electrical charges, electric fields, and the fundamental structure of matter.
Electrostatic Force: Electrostatic force is the attractive or repulsive force that exists between stationary electric charges. It is a fundamental force in nature that governs the interactions between charged particles, and it is a key concept in understanding the behavior of electric fields and Coulomb's law.
Equipotential Surface: An equipotential surface is a surface in an electric field where the electric potential is constant. In other words, all points on an equipotential surface have the same electric potential, meaning no work is required to move a charged particle along this surface.
Field Line: A field line is a graphical representation of the direction and strength of a force field, such as an electric or magnetic field, at different points in space. Field lines provide a visual aid to understand the overall structure and behavior of the field.
Gauss: Gauss is a unit of measurement used to quantify the strength of a magnetic field. It is named after the renowned German mathematician and physicist Carl Friedrich Gauss, who made significant contributions to the understanding of electromagnetism.
Maxwell's Equations: Maxwell's equations are a set of four fundamental equations in electromagnetism that describe the relationships between electric and magnetic fields and electric charges and currents. These equations form the foundation for the study of classical electromagnetism and are essential in understanding the behavior of electromagnetic waves, including light.
Newton per Coulomb: Newton per coulomb (N/C) is a unit that measures the strength of an electric field. It represents the force exerted on a unit positive charge placed in an electric field, quantifying the intensity of the electric field at that point.
Permittivity: Permittivity is a fundamental property of a material that describes its ability to transmit and store electric fields. It is a measure of the electric polarization that occurs when an electric field is applied to a material, and it plays a crucial role in the behavior of electric fields within and around that material.
Point Charge: A point charge is an idealized model of an electric charge that is concentrated at a single point in space, with no spatial extent. It is a fundamental concept in electrostatics and is used to describe the electric field and electric potential generated by a localized electric charge.
Polarization: Polarization refers to the orientation or alignment of the electric field component of electromagnetic radiation. It describes the direction in which the electric field oscillates as the wave propagates through space.
Potential Energy: Potential energy is a form of energy that an object possesses due to its position or state, rather than its motion. It is the stored energy an object has the potential to release or convert into other forms of energy, such as kinetic energy or thermal energy.
Proton: A proton is a subatomic particle that carries a positive electric charge and is a fundamental component of all atomic nuclei. Protons are crucial in understanding the concepts of electrical charges, electric fields, and the structure of matter at the most fundamental level.
Superposition: Superposition is the principle that when two or more waves interact, the resulting wave pattern is the sum of the individual wave patterns. This concept applies to various types of waves, including sound waves, electromagnetic waves, and waves in physical media such as water and air.
Unit Vector: A unit vector is a vector with a magnitude of 1 that points in a specific direction. It is used to represent the direction of a vector without regard to its magnitude.
Vector Sum: The vector sum, also known as the resultant vector, is the combined effect of two or more vectors acting on an object. It represents the net displacement, force, or quantity when multiple vectors are added together geometrically.
Volt per Meter: Volt per meter (V/m) is a unit used to measure the strength or magnitude of an electric field. It represents the potential difference or voltage drop per unit distance within an electric field, providing a quantitative assessment of the electric force acting on charged particles in that field.
Work: Work is a fundamental concept in physics that describes the transfer of energy through the application of a force over a distance. It represents the amount of energy required to move an object a certain distance in the direction of the applied force, and is a crucial factor in understanding energy transformations and the laws of motion.
ε₀: ε₀, also known as the permittivity of free space or the vacuum permittivity, is a fundamental physical constant that represents the ability of free space, or a vacuum, to support an electric field. It is a measure of the electric flux density per unit electric field strength in a vacuum and is a crucial parameter in various electromagnetic phenomena and calculations.